Duke Mathematical Journal

Commensurability of co-compact three-dimensional hyperbolic groups

A. M. Macbeath

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J. Volume 50, Number 4 (1983), 1245-1253.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 11F06: Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 53C35: Symmetric spaces [See also 32M15, 57T15] 57N10: Topology of general 3-manifolds [See also 57Mxx] 57S99: None of the above, but in this section


Macbeath, A. M. Commensurability of co-compact three-dimensional hyperbolic groups. Duke Math. J. 50 (1983), no. 4, 1245--1253. doi:10.1215/S0012-7094-83-05054-8. http://projecteuclid.org/euclid.dmj/1077303499.

Export citation


  • [1] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Funktionen, Vol. 1, p. 335 ff. (Teubner, Leipzig, 1897, reprint Johnson, New York, 1965).
  • [2] T. Jørgensen, Compact $3$-manifolds of constant negative curvature fibering over the circle, Ann. Math. (2) 106 (1977), no. 1, 61–72.
  • [3] F. Lannér, On complexes with transitive groups of automorphisms, Comm. Sém., Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 11 (1950), 71.
  • [4] A. M. Macbeath, Generators of the linear fractional groups, Number Theory (Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967), Amer. Math. Soc., Providence, R.I., 1969, pp. 14–32.
  • [5] G. D. Mostow, Strong rigidity of locally symmetric spaces, Princeton University Press, Princeton, N.J., 1973.
  • [6] A. Weil, On discrete subgroups of Lie groups, Ann. of Math. (2) 72 (1960), 369–384.

See also

  • See also: A. M. Macbeath. Erratum: “Commensurability of co-compact three-dimensional hyperbolic manifolds,” vol. 50 (1983) pp. 1245–1253. Duke Math. J. Vol. 56, No. 1 (1988), pp. 219–219.